In school, I was taught that the speed of light is constant, in the sense that if you shoot a laser off of a train going 200 km/h, it still just goes at a speed of c=299,792,458 m/s, not at c + 200 km/h.
What confuses me about this, is that we're constantly on a metaphorical train:
The Earth is spinning and going around the sun. The solar system is going around the Milky Way. And the Milky Way is flying through the universe, too.
Let's call the sum of those speeds v_train.
So, presumably if you shoot a laser into the direction that we're traveling, it would arrive at the destination as if it was going at 299,792,458 m/s - v_train.
The light is traveling at a fixed speed of c, but its target moves away at a speed of v_train.
This seems like it would have absolutely wild implications.
Do I misunderstand something? Or is v_train so small compared to c that we generally ignore it?
You're looking for an absolute standard vector, to measure absolute velocities?
Yes, I think you can make one. It's not even hard. But how can you tell wether you are moving, or wether it is moving?
Imagine all the possible ways this vector can be in, and move through space. For all of those, you measure the same speed of light. But for each of those, you measure a different wavelength, based on it's relative speed (and due to the universe expanding, distance) to you.
Now you can tell your relative distance and speed to any of these vectors. Like we do with other astronomical objects.
If you want to get rid of relativeness, and achieve absoluteness, you have to subjectively define which reference frame is your rest frame.
I guess that makes sense, but I was always struck by the assertion that there is no absolute reference frame for our universe. If the speed of light in a vacuum is a constant speed, that always struck me as incompatible in my head because the speed of light itself would define an absolute reference frame. I'm certainly not trying to assert anything, and I assume I'm just not understanding it properly, but a universe wide constant that can be used to define a vector feels like it could be used to establish a zero coordinate. If you could establish three points that are not moving relative to each other and measure their universal velocities, a difference between the three axes of velocity could point to a spherical center point.
Yes. Maybe a key point is to think about "speed relative to what?". Maybe we like to think about speed relative to an objective, unmoving, unchanging background. Sort of like the big stage on which the universe plays. Like a level in a video game, where each object has absolute coordinates and velocities relative to 'the universe itself'.
But in reality, we have no such thing. Or it depends on what we define as that background.
How exactly? I invite you to work out the details, make a geometry sketch.
Yes, we can use the speed of light to define a vector. For example, 1 light year is such a vector. Or 1 light second. Ah no, those are merely 1-dimensional distances. We surely can construct 3-dimensional vectors from them, though. But what is this vector's null rotation? And where is the origin of our coordinate system? A vector can be rotated and translated arbitrarily, and still be the same vector.